The area of the region, inside the ellipse $x^{2}+4y^{2}=4$ and outside the region bounded by the curves $y=|x|-1$ and $y=1-|x|$, is:

If the area of the region $S=\{(x, y): 2y - y^2 \leq x^2 \leq 2y, x \geq y\}$ is equal to $\frac{n+2}{n+1} - \frac{\pi}{n-1}$,then the natural number $n$ is equal to $...............$.

The area of the region given by $A = \{(x, y) : x^{2} \leq y \leq \min \{x+2, 4-3x\}\}$ is:

Calculate the area enclosed by the curves $x^2 = 2 - y$ and $x^2 = y$.

The area (in sq. units) of the region enclosed by the curves $y=x^{2}-1$ and $y=1-x^{2}$ is equal to

Let $f :[-3,1] \rightarrow R$ be given as
$f(x)=\begin{cases} \min \{(x+6), x^{2}\}, & -3 \leq x \leq 0 \\ \max \{\sqrt{x}, x^{2}\}, & 0 \leq x \leq 1 \end{cases}$
If the area bounded by $y = f(x)$ and the $x$-axis is $A$,then the value of $6A$ is equal to ....... .